Mod p representations of SL2(Qp)

In Barthel and Livne (1994) [3], , the authors give a rough classification of mod p representations of GL2(F) where F is a finite extension of Qp. In Breuil (2003) [4], the author gives a complete classification of mod p representations of GL2(Qp). In this paper, using the classification in those two papers, we classify mod p representations of SL2(Qp). We also define conductors and newforms for these representations and compute the conductors and the dimensions of spaces of newforms.